3/11/2024 0 Comments Limit chain ruleOkay let's try this out on h of x equals e to the x squared plus 3x+1 and let's observe that again the outside function is e to the x and the inside function is this polynomial x squared plus 3x+1 and so the derivative according to this formula is the same function e to the g of x right so e to the x squared plus 3x+1 times g prime of x and that's the derivative of the inside function.Īnd that derivative is 2x+3 and that's it, these are super easy to differentiate so every time you a function of the form e to the g of x it's derivative is e to the g of x times the derivative of the inside function. And this is because the derivative of e to the x if you'll recall derivative of e to the x is just e to the x. So the derivative of e to the g of x is e to the g of x times g prime of x. This value can be any point on the number line and often limits are. we'll have e to the x as our outside function and some other function g of x as the inside function.Īnd I'll have a special version of the chain rule that I'll use for these and I'll call this rule the general exponential rule. The limit is a method of evaluating an expression as an argument approaches a value. I want to talk about a special case of the chain rule where the function that we're differentiating has its outside function e to the x so in the next few problems we're going to have functions of this type which I call general exponential functions.
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